The present invention relates to a new and distinct fall bearing raspberry variety designated as ‘GLEAM’. This new variety is a result of a controlled cross made in 2005 in Watsonville, Calif. between raspberry variety ‘PS-1852’ (patented, U.S. Plant Pat. No. 18,806) as the female parent and raspberry variety ‘RADIANCE’ (patented, U.S. Plant Pat. No. 20,342) as the male parent in an ongoing breeding program. The variety is botanically known as Rubus idaeus. 
The seedling resulting from the aforementioned cross was asexually propagated by dormant canes in Santa Cruz County, Calif. and was subsequently selected by the inventor from a controlled breeding plot in Watsonville, Calif. in 2007. After its selection, the new variety was further asexually propagated by dormant canes, roots and non-dormant root shoot cuttings in Santa Cruz County, Calif., San Joaquin County, Calif. and Siskiyou County, Calif. The new variety was then extensively tested over the next several years in fruiting fields in Santa Cruz County, Calif. This propagation has demonstrated that the combination of traits disclosed herein as characterizing the new variety are fixed and remain true to type through successive generations of asexual reproduction.